For a parallelogram , consecutive
angles are supplementary (P + Q = 180°).∠P +∠Q =180°4∠Q + ∠Q =180°
(Since angle P is four times angle Q)5(∠Q) = 180 degree∠Q = 180/5 =36 degreeTherefore ∠P
=144 degreeFor paralleogram opposite angles are
equal. So ∠R
=144 degree
9. The population of a town increases by 5% every year .If the present
population is 9261, the population 3 years ago was: Ans: 8000Solution:This can be solved by Compound interest equation.CI= 9261R=5%n=3CI= P(1+ R/100)n10. The average weight of 15 oarsmen in a boat is increased by 1.6kg when
one of the crew,who weighs 42kg is replaced by a new man. Find the weight of
new man.(in kg).Ans: 66 kg.Solution:It is clear that new man has more weight than earlier one.Total increase in weight= 1.6kg x 15 = 24kgWeight of new man = 42+24= 66kg.11. the sides of a triangle having area 7776 sq.cm are in the ratio 3:4:5.
the perimeter of the traingle is :Ans: 432cm.Solution:Let the length of sides be 3x , 4x, 5xSide 5x is the hypotenuse. Area = 1/2bh = 1/2 (3x)(4x) = 6x2
So, 6x2=7776Solving x=36.Length of Sides are 108cm, 144cm , 180cm.Perimeter = 108+144+180 = 432sm.
12. The measure of an angle whose supplement is three times as large as
its complement, isa)30 degree b) 45 degree c) 60 degree d) 75 degreeAns: 45 degree 12. FInd the value of tan40 tan430 tan470 tan860 Ans: 1Solutiontan(86) = tan(90-86) =cot(4)tan(47) = tan(90-47) = cot (43)so, tan4 tan 43 cot 43 cot 4 = (tan4 cot 4 )( tan
43 cot 43) =113. A ship after sailing 12 km towards south from a particular place covered
5km more towards east. Then the straight way distance of the ship from the
place is :Ans: 13kmSolution:The distance will be the length of line joining initial points.
It can be found out by pythagoras theorem.Distance = √(122 + 52)
= 13.

14. Two poles of height 7m and 12m stand on plane ground. If the
distance between the feet is 12m, the distance between their top will be:
Ans: 13mSolution: